Abstract: This paper reports some rather surprising interim results concerning the optimization of arches designed for either single or alternate loads and subject to both bending and axial compression. The current work will be later extended to surface structures, such as archgrids and cable networks. This note also demonstrates the power and versatility of the prager-shield optimality criteria. Although only trivially simple problems are considered herein for educational reasons, the same methods have been found to be very effective for more complicated loading conditions.